Why do we need explainable AI?
As argued by Selvaraju et al., there are three stages of AI evolution, in all of which interpretability is helpful. 


In the early stages of AI development, when AI is weaker than human performance, transparency can help us build better models. It can give a better understanding of how a model works and helps us answer several key questions. For example why a model works in some cases and doesn't in others, why some examples confuse the model more than others, why these types of models work and the others don't, etc.
When AI is on par with human performance and ML models are starting to be deployed in several industries, it can help build trust for these models. I'll elaborate a bit on this later, because I think that it is the most important reason.
When AI significantly outperforms humans (e.g. AI playing chess or Go), it can help with machine teaching (i.e. learning from the machine on how to improve human performance on that specific task).


Why is trust so important?

First, let me give you a couple of examples of industries where trust is paramount:


In healthcare, imagine a Deep Neural Net performing diagnosis for a specific disease. A classic black box NN would just output a binary "yes" or "no". Even if it could outperform humans in sheer predictability, it would be utterly useless in practice. What if the doctor disagreed with the model's assessment, shouldn't he know why the model made that prediction; maybe it saw something the doctor missed. Furthermore, if it made a misdiagnosis (e.g. a sick person was classified as healthy and didn't get the proper treatment), who would take responsibility: the model's user? the hospital? the company that designed the model? The legal framework surrounding this is a bit blurry.
Another example are self-driving cars. The same questions arise: if a car crashes whose fault is it: the driver's? the car manufacturer's? the company that designed the AI? Legal accountability, is key for the development of this industry.


In fact, this lack of trust, has according to many hindered the adoption of AI in many fields (sources: 1, 2, 3). While there is a running hypothesis that with more transparent, interpretable or explainable systems users will be better equipped to understand and therefore trust the intelligent agents (sources: 1, 2, 3). 

In several real world applications you can't just say "it works 94% of the time". You might also need to provide a justification...

Government regulations

Several governments are slowly proceeding to regulate AI and transparency seems to be at the center of all of this. 

The first to move in this direction is the EU, which has set several guidelines where they state that AI should be transparent (sources: 1, 2, 3). For instance the GDPR states that if a person's data has been subject to "automated decision-making" or "profiling" systems, then he has a right to access


  "meaningful information about the logic involved"


(Article 15, EU GDPR)

Now this is a bit blurry, but there is clearly the intent of requiring some form of explainability from these systems. The general idea the EU is trying to pass is that "if 
 you have an automated decision-making system affecting people's lives then they have a right to know why a certain decision has been made." For example a bank has an AI accepting and declining loan applications, then the applicants have a right to know why their application was rejected.

To sum up...

Explainable AIs are necessary because:


It gives us a better understanding, which helps us improve them.
In some cases we can learn from AI how to make better decisions in some tasks.
It helps users trust AI, which which leads to a wider adoption of AI.
Deployed AIs in the (not to distant) future might be required to be more "transparent".